Probabilistic Tracking Control Method, Medium and Device for Maglev Train Levitation System

Abstract

The present invention provides a probabilistic tracking control method, medium and device for a maglev train suspension system, belonging to the technical field of suspension control. The method includes: constructing a target probability density function of the controlled quantity of the suspension system; taking the minimization of a set loss function as the goal, training the probability density function of the controlled quantity output by the physics-informed neural network by using the target probability density function, so that the probability density function of the controlled quantity output by the physics-informed neural network approximates the target probability density function, and optimizing the control force in the control input of the suspension system; using the optimized control force to design a feedback control force for adjusting the probability density function of the controlled quantity of the suspension system to achieve the control goal. The present invention can effectively handle complex disturbances caused by various interferences, and can be widely applied to rail transit systems such as maglev trains, especially for suspension control under complex disturbances, improving the suspension stability, safety and operation efficiency of maglev trains.

Description

Technical Field

[0001] The present invention relates to the technical field of suspension control, and more specifically, to a probabilistic tracking control method, medium, and device for a maglev train suspension system. Background Art

[0002] Maglev trains play an important role in modern rail transit due to their advantages such as low noise, strong climbing ability, and small turning radius. However, the suspension system of maglev trains faces many challenges during actual operation. For example, maintaining the dynamic stability of the suspension gap under time-varying disturbances is one of the key issues. A stable suspension gap oscillation is crucial for the normal operation of the suspension system, and precise regulation of the suspension gap within an acceptable range is required. Due to the inherent nonlinear dynamic characteristics of the suspension system and the influence of random excitations such as track irregularities, foundation settlement, and wind load disturbances, the dynamic behavior of the system becomes complex, which may lead to an increase in suspension gap fluctuations, enhanced vibrations, and even instability, thereby affecting the running safety and riding comfort of the train.

[0003] In the prior art, suspension control schemes mainly focus on deterministic systems or systems only affected by continuous random excitations, while relatively few studies have been conducted on random disturbances caused by jump noises (such as track steps). Jump noises can cause sudden changes in system states, affect the stability and reliability of the suspension system, and significantly increase the complexity of control. Therefore, existing control methods based on continuous random disturbances are difficult to effectively handle the complex dynamic behavior under the combined action of Gaussian white noise and Poisson white noise. In addition, due to the existence of random excitations, stochastic control of the suspension system is crucial. The main objectives of stochastic control are system response control, including strategies such as moment control and probabilistic tracking control. Since the probability density function can completely describe the statistical characteristics of system responses, while finite-order moments can only provide partial information, probabilistic tracking control has become an important research direction in stochastic control. Probabilistic tracking control methods aim to make the probability density function of the controlled system consistent with the target probability density function. Existing probabilistic tracking control methods mainly rely on analytical methods or numerical calculation methods to solve the Fokker-Planck-Kolmogorov equation. These methods are extremely difficult to solve under the action of nonlinear systems and non-Gaussian noises, have high computational complexity, and are difficult to ensure control accuracy, making them unsuitable for real-time control requirements in actual control engineering.

[0004] In summary, it is necessary to improve the prior art to solve the probabilistic tracking control problem of the suspension system of maglev trains under the excitation of different types of noises. Summary of the Invention

[0005] The object of the present invention is to overcome the defects of the above prior art and provide a probabilistic tracking control method, medium, and device for a maglev train suspension system.

[0006] According to a first aspect of the present invention, there is provided a probabilistic tracking control method for a maglev train levitation system. The method includes the following steps:

[0007] Construct a target probability density function of the controlled quantity of the levitation system;

[0008] With the goal of minimizing a set loss function, use the target probability density function to train the probability density function of the controlled quantity output by the physics-informed neural network, so that the probability density function of the controlled quantity output by the physics-informed neural network approximates the target probability density function, and optimize the control force in the control input of the levitation system;

[0009] Use the optimized control force to design a feedback control force for adjusting the probability density function of the controlled quantity of the levitation system to achieve the control goal;

[0010] Wherein, the physics-informed neural network includes a first deep neural network and a second deep neural network. The first deep neural network is used to fit the probability density function of the controlled quantity of the levitation system, and the second deep neural network is used to fit the control force of the probability density function of the controlled quantity.

[0011] According to a second aspect of the present invention, there is provided a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the probabilistic tracking control method for the maglev train levitation system provided in the first aspect is implemented. [[ID=!

[0012] According to a third aspect of the present invention, there is provided a computer device, including a memory and a processor. A computer program capable of running on the processor is stored on the memory. When the processor executes the computer program, the steps of the probabilistic tracking control method for the maglev train levitation system provided in the first aspect are implemented.

[0013] Compared with the prior art, the advantages of the present invention are that the provided probabilistic tracking control method for the maglev train levitation system uses probabilistic tracking control based on a physics-informed neural network to solve the problem that existing methods are only applicable to deterministic systems or systems only affected by continuous random excitations and are difficult to effectively cope with the combined random excitation of Gaussian and Poisson white noises, and significantly improves the adaptability of the controlled system to complex random disturbances.

[0014] Through the following detailed description of the exemplary embodiments of the present invention with reference to the accompanying drawings, other features and advantages of the present invention will become clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The drawings incorporated in the specification and constituting a part of the specification illustrate embodiments of the present invention and, together with the description, are used to explain the principles of the present invention.

[0016] Figure 1 It is a flowchart of the probability tracking control method for the maglev train suspension system according to an embodiment of the present invention;

[0017] Figure 2 It is a schematic diagram of the process of the probability tracking control method for the maglev train suspension system according to an embodiment of the present invention;

[0018] Figure 3 It is a schematic diagram of the structure of the physical information neural network model according to an embodiment of the present invention;

[0019] Figure 4 It is a schematic diagram of the structure of the single-point suspension system according to an embodiment of the present invention;

[0020] In the drawings, 1 - suspension electromagnet; 2 - track step; 3 - track; PD - proportional derivative. Detailed implementation manners

[0021] Now, various exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that: Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention.

[0022] The following description of at least one exemplary embodiment is merely illustrative in nature and in no way serves as a limitation on the present invention, its application, or its use.

[0023] Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such technologies, methods, and devices should be regarded as part of the specification.

[0024] In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0025] It should be noted that: Similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0026] Combined with Figure 1 and Figure 2 As shown, the provided probability tracking control method for the maglev train suspension system includes the following steps:

[0027] Step S110, construct the target probability density function of the controlled quantity of the suspension system and the physical information neural network model.

[0028] For example, based on physical or engineering requirements, actual operation data of the system, or theoretical models, calculate the target probability density function of the controlled quantity of the suspension system.

[0029] In one embodiment, the physics-informed neural network model includes at least two deep neural networks. Taking two deep neural networks as an example, or referred to as the first deep neural network and the second deep neural network, where the first deep neural network is used to approximate the probability density function of the controlled quantity of the suspension system, and the second deep neural network is used to approximate the control force of the probability density function of the controlled quantity. The controlled quantity includes but is not limited to the vertical acceleration of the car body of the suspension system, the suspension gap, the train operation smoothness index, the control performance index, etc.

[0030] See Figure 3 As shown, the input quantities of the input layers of the two deep neural networks are both two, including the deviation of the controlled quantity of the suspension system and the deviation of the derivative of the controlled quantity with respect to time . The output quantities of the output layers are both one, which are the probability density function of the controlled quantity and the control force for controlling the probability density function of this quantity . Figure 3 In , represents the activation process, represents the parameters of the first deep neural network, represents the parameters of the second deep neural network, represents the derivative.

[0031] Step S120, with the minimization of the set loss function as the optimization goal, use the target probability density function to train the probability density function of the controlled quantity output by the physics-informed neural network, so that the probability density function of the controlled quantity output by the physics-informed neural network approximates the target probability density function, and optimize the control force in the control input of the suspension system.

[0032] In this step, use the target probability density function to train the probability density function of the controlled quantity output by the physics-informed neural network, so that the probability density function of the controlled quantity output by the neural network approximates the target probability density function, and optimize the control force in the control input of the suspension system until the set loss function criterion is met, for example, the loss function minimization criterion.

[0033] In one embodiment, the loss function of the physics-informed neural network includes the error term between the trained probability density function of the controlled quantity and the target probability density function and the error term of the residual of the forward Kolmogorov equation , which are respectively expressed as:

[0034] (1)

[0035] (2)

[0036] Among them, is the number of training points for the target probability density function; and denote the state variables at the i -th training point among ( ) training points, corresponding to the deviation of the controlled variable and the deviation of the time derivative of the controlled variable respectively; is the output of the neural network used to approximate the probability density function of the controlled variable, is the target probability density function; is the number of training points for the forward Kolmogorov equation; and denote the state variables at the i -th training point among ( ) is the output of the neural network used to fit the control force, is the neural network parameter; the function [ ; ] represents the residual expression obtained by substituting the neural network output into the forward Kolmogorov equation.

[0037] Specifically, the target probability density function of the controlled variable of the suspension system is calculated based on physical engineering requirements, actual system operation data, or theoretical models. A physics-informed neural network model is used to learn and approximate the solution of the forward Kolmogorov equation, that is, the actual probability density function of the system's controlled variable. The two deep neural networks in the physics-informed neural network model interact with each other during the training process. By minimizing the loss function of the neural network, the optimal control force is found, so that the actual probability density function of the system's controlled variable approaches the target probability density function, realizing probability tracking control.

[0038] Combined with Figure 3 shown, the interaction between the two deep neural networks during the training process is specifically manifested as follows: during the training process, the neural network adjusts the control force in the control input to make the neural network approach the target probability density function. The neural network provides information on the actual probability density function of the controlled variable of the suspension system, and guides in reverse to generate a better control strategy. The two deep neural networks interact with each other and jointly optimize the control input, so that the probability density function of the controlled variable of the suspension system is stabilized near the target probability density function, improving the stability of the system.

[0039] To further improve the training accuracy of the physics-informed neural network, during the training process, an adaptive sampling method can be used to obtain training points.

[0040] Still in combination with Figure 2 and Figure 3 As shown, the neural network input quantity sampling set includes two groups of points: the first group is the forward Kolmogorov equation training points, with a quantity of for calculating the error term of the forward Kolmogorov equation residual in the loss function. The second group is the target probability density function training points, with a quantity of for calculating the error term between the controlled quantity probability density function of the network output and the target probability density function in the loss function.

[0041] In one embodiment, the first group of sampling sets is sampled using a uniform sampling method (such as Latin hypercube sampling), and the second group of sampling sets is sampled using an adaptive sampling method based on the target probability density function. The adaptive sampling method first uses uniform sampling and Hamiltonian Monte Carlo sampling to obtain some initial training points, and then during the neural network training process, the remaining training points are sampled multiple times using the adaptive sampling strategy to update the training points.

[0042] Specifically, the adaptive sampling method based on the target probability density function includes the following steps:

[0043] Step 1, select a certain number of training points in the input space through uniform sampling (such as Latin hypercube sampling method) and Hamiltonian Monte Carlo sampling method, and use these points to train the physics-informed neural network to output the probability density function of the controlled quantity at these training points.

[0044] Step 2, use the adaptive sampling strategy for sampling. First, divide the input space into multiple subdomains, calculate the sum of the absolute values of the forward Kolmogorov equation residuals at all training points in each subdomain and find the average value. Then, for the subdomain with the largest average absolute residual, add a certain number of training points in this subdomain and add the newly added training points to the second group of sampling sets, that is, the training points for the target probability density function.

[0045] Preferably, the adaptive sampling strategy selects more training points in the subdomains with larger forward Kolmogorov equation residuals and adds these training points to the loss function, directly as the training points for the error term between the controlled quantity probability density function of the neural network output and the target probability density function.

[0046] Step S130, use the optimized control force to design a feedback control force for adjusting the controlled quantity probability density function of the suspension system to achieve the control target.

[0047] In the actual application of the model, the trained physics-informed neural network can be used to obtain optimized control forces, and then the probabilistic tracking control of the suspension system can be realized by designing a feedback control strategy.

[0048] To further verify the effectiveness of the present invention, experimental verification was carried out. The hardware and software devices used for verification include the sensing device for collecting the controlled variables of the actual maglev train suspension system, the training program of the physics-informed neural network model, the program for calling the suspension system model, the adaptive sampling strategy program, the signal acquisition device of the actual maglev train suspension system, etc.

[0049] Taking the controlled variable as the suspension gap of the maglev train suspension system and setting the target probability density function of the suspension gap according to the engineering requirements as an example, the specific implementation steps of the probabilistic tracking control method based on the physics-informed neural network are provided in the experimental verification process.

[0050] Since the controlled variable is the dynamic response of the suspension system in the vertical direction, that is, the vehicle body suspension gap, the suspension system can be simplified to a single-point suspension system. The structure of the single-point suspension system is as Figure 4 shown. According to the structure of the single-point suspension system, the dynamic equation of the single-point suspension system can be further established. The PD (Proportional-Differential control) control strategy is adopted to adjust the current magnitude of the suspension system, so as to make the suspension system stably suspended. According to the dynamic equation and control law of the single-point suspension system, the forward Kolmogorov equation is further obtained. The target probability density function of the suspension gap is obtained according to the actual engineering requirements. The training points of the forward Kolmogorov equation are obtained by using the Latin hypercube sampling method, and some initial training points of the target probability density function are obtained by using the Latin hypercube sampling method and the Hamiltonian Monte Carlo sampling method. The physics-informed network model is trained, and the remaining training points of the target probability density function are obtained by using the adaptive sampling strategy during the training. The neural network is trained for 10,000 rounds in total, and the training points are updated every 500 rounds by using the adaptive sampling strategy. When the neural network is trained for 10,000 rounds, the probability density function of the suspension gap and the control force of the control probability density function are output. Furthermore, the obtained control force can be used in the system control input, so that the probability density function of the suspension gap of the suspension system is stabilized near the target probability density function to improve the stability of the suspension system.

[0051] In summary, compared with the prior art, the present invention has the following advantages:

[0052] 1) By combining the physics-informed neural network with the forward Kolmogorov equation, the present invention uses two deep neural networks to obtain the probability density function of the controlled quantity and the control force respectively. By integrating the forward Kolmogorov equation into the structure of the physics-informed neural network, it allows for an accurate approximation of the objective function, avoiding the solution of the forward Kolmogorov equation by analytical methods or numerical calculation methods, avoiding the direct calculation of this equation, greatly improving the calculation efficiency, and reducing the consumption of computing resources.

[0053] 2) The present invention can adapt to different types of noise, including but not limited to Gaussian and Poisson white noise, ensuring the stability of the system under different perturbations.

[0054] 3) The present invention can automatically adjust the control input through a neural network optimization algorithm, improving the stability and response accuracy of the maglev train suspension system.

[0055] 4) The present invention proposes an adaptive sampling method based on the target probability density function, increasing the training points in the region where the residual of the forward Kolmogorov equation is large, thereby improving the network's learning ability in the region where the probability density function is difficult to fit, and improving the network training efficiency and control accuracy.

[0056] 5) The present invention is generally applicable to medium- and low-speed maglev trains and can be applied to high-speed maglev trains and other rail transit systems. Especially in the face of complex track environments and random perturbations, it can effectively control the stability of the suspension system.

[0057] The present invention can be a system, a method, and / or a computer program product. The computer program product may include a computer-readable storage medium having thereon computer-readable program instructions for causing a processor to implement various aspects of the present invention.

[0058] A computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. A computer-readable storage medium may be, for example, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanically encoded device such as a punched card or raised structures in grooves having instructions stored thereon, and any suitable combination of the foregoing. The computer-readable storage medium as used herein is not construed to be a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., an optical pulse through an optical fiber cable), or an electrical signal transmitted through a wire.

[0059] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to various computing / processing devices, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network may include a copper transmission cable, an optical fiber transmission, a wireless transmission, a router, a firewall, a switch, a gateway computer, and / or an edge server. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium in each computing / processing device.

[0060] The computer program instructions for performing the operations of the present invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine - related instructions, microcode, firmware instructions, state - setting data, or source code or object code written in any combination of one or more programming languages, including object - oriented programming languages such as Smalltalk, C++, Python, etc., and conventional procedural programming languages such as the "C" language or similar programming languages. The computer - readable program instructions may be executed entirely on the user's computer, partially on the user's computer, executed as a stand - alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider). In some embodiments, by using the state information of the computer - readable program instructions to customize an electronic circuit, such as a programmable logic circuit, a field - programmable gate array (FPGA), or a programmable logic array (PLA), the electronic circuit can execute the computer - readable program instructions to implement various aspects of the present invention.

[0061] Aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer - readable program instructions.

[0062] These computer - readable program instructions can be provided to a processor of a general - purpose computer, a special - purpose computer, or other programmable data - processing apparatus to produce a machine such that the instructions, when executed by the processor of the computer or other programmable data - processing apparatus, create a means for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram. These computer - readable program instructions can also be stored in a computer - readable storage medium that causes a computer, a programmable data - processing apparatus, and / or other devices to function in a particular manner, so that the computer - readable medium storing the instructions comprises a manufacture including instructions for implementing various aspects of the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0063] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device, causing a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process such that the instructions executed on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0064] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two consecutive blocks may in fact be executed substantially in parallel, or they may sometimes be executed in the reverse order, depending on the functionality involved. It should also be noted that each block of the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system that performs the specified functions or acts, or by a combination of dedicated hardware and computer instructions. As will be apparent to those of ordinary skill in the art, implementations through hardware, through software, and through a combination of software and hardware are equivalent.

[0065] The embodiments of the present invention have been described above. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the market, or to enable other ordinary skilled persons in the art to understand the embodiments disclosed herein. The scope of the present invention is defined by the appended claims.

Claims

1. A probabilistic tracking control method for a maglev train suspension system, comprising the following steps: Construct the target probability density function of the controlled quantity of the suspension system; With the goal of minimizing a set loss function, the controlled variable probability density function output by the physical information neural network is trained using the target probability density function, so that the controlled variable probability density function output by the physical information neural network approaches the target probability density function, and the control force in the suspension system control input is optimized; Using the optimized control force, a feedback control force is designed to adjust the probability density function of the controlled variable of the suspension system to achieve the control target. The physical information neural network includes a first deep neural network and a second deep neural network, the first deep neural network is used to fit the controlled quantity probability density function of the suspension system, and the second deep neural network is used to fit the control force of the controlled quantity probability density function; In which, during the training process of the physical information neural network, the second deep neural network adjusts the control force in the control input so that the first deep neural network approaches the target probability density function. The first deep neural network provides the actual probability density function information of the controlled quantity, and reversely guides the second deep neural network to generate a better control force, so that the error between the probability density function of the controlled quantity and the target probability density function reaches the set standard by jointly optimizing the control input.

2. The method according to claim 1, characterized in that The controlled variables include one or more of the vertical acceleration of the suspension system vehicle body, the suspension gap, the train running stability index and the control performance index.

3. The method according to claim 1, wherein The loss function includes the error terms of the controlled variable probability density function and the target probability density function obtained through training, as well as the error term of the forward Kolmogorov equation residual.

4. The method according to claim 1, wherein For the first deep neural network, the input quantity of its input layer is the deviation of the controlled quantity and the deviation of the controlled quantity with respect to the time derivative, and the output quantity of the output layer is the probability density function of the controlled quantity; for the second deep neural network, the input quantity of its input layer is the deviation of the controlled quantity and the deviation of the controlled quantity with respect to the time derivative, and the output quantity of the output layer is the control force of the probability density function of the controlled quantity.

5. The method according to claim 3, wherein During the training process of the physical information neural network, the input quantity sampling set includes a first group of sampling sets and a second group of sampling sets. The first group of sampling sets are the forward Kolmogorov equation training points, which are used to calculate the error term of the forward Kolmogorov equation residual in the loss function. The second group of sampling sets are the target probability density function training points, which are used to calculate the error term of the controlled quantity probability density function and the target probability density function in the loss function.

6. The method according to claim 5, wherein The first sampling set is sampled using uniform sampling, and the second sampling set is sampled using an adaptive sampling method based on the target probability density function.

7. The method according to claim 6, wherein The adaptive sampling based on the target probability density function includes: dividing the input space into multiple subdomains, calculating the sum of the absolute values of the forward Kolmogorov equation residuals at all training points in each subdomain, and taking the average value; for the subdomain with the largest average residual absolute value, adding a set number of training points in the subdomain, and adding the added training points to the second sampling set.

8. A computer-readable storage medium having a computer program stored thereon, wherein, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer device, comprising a memory and a processor, wherein a computer program capable of running on the processor is stored on the memory, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

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